Biomechanics and Modeling in Mechanobiology

, Volume 11, Issue 7, pp 995–1000

A perturbation solution of the mechanical bidomain model


    • Department of PhysicsOakland University
  • Bradley J. Roth
    • Department of PhysicsOakland University
Original Paper

DOI: 10.1007/s10237-011-0368-1

Cite this article as:
Punal, V.M. & Roth, B.J. Biomech Model Mechanobiol (2012) 11: 995. doi:10.1007/s10237-011-0368-1


This research focuses on finding analytical solutions to the mechanical bidomain model for cardiac tissue. In particular, a perturbation expansion is used to analyze the equations, with the perturbation parameter being inversely proportional to the spring constant coupling the intracellular and extracellular spaces. The results indicate that the intracellular and extracellular pressures are not equal and that the two spaces can move relative to each other. This calculation is complicated enough to illustrate the implications of the mechanical bidomain model but is nevertheless simple enough to solve analytically. One application of the calculation is to the mechanical behavior of active cardiac tissue surrounding an ischemic region.


Mechanical bidomainCardiac tissuePerturbation expansionPressureStream function
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© Springer-Verlag 2011